BER Estimation of Dual-hop PSK OFDM RoFSO Communication System over K or NE Modeled Turbulence and Optical Fiber with Nonlinear Clipping Effect

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1 BER Estimatio of Dual-hop PSK OFDM RoFSO Commuicatio System over K or E Modeled Turbulece ad Optical Fiber with oliear Clippig Effect A.D. Tsigopoulos 1, M.P. ios, A.. Stassiakis 1 Sectio of Battle Systems, aval Operatios, Sea Studies, avigatio, Electroics ad Telecommuicatios, Helleic aval Academy, Hadjikyriakou ave, Piraeus 18539, Greece, atsigo@sd.edu.gr Dept. of Electroics, Computers, Telecommuicatios ad Cotrol, Faculty of Physics, atioal ad Kapodistria Uiversity of Athes, Athes, 15784, Greece, s: {a-stassiakis; imichail}@phys.uoa.gr Abstract. Radio o free space optics (RoFSO) is a techology similar to the Radio over Fiber (RoF) commuicatio systems, which eables the trasmissio of radio frequecy sigals (RF) i the optical domai through the free space. As a cosequece, high capacity liks are implemeted with low operatioal ad istallatio costs ad without eed of licese for spectrum use. However, their performace depeds strogly o the atmospheric coditios ad the radom chages of the propagatio medium characteristics. O the other had, usig RoF liks we ca achieve higher badwidths over loger distaces but with the requiremet of optical fiber ifrastructure. I this work, we ivestigate the bit error rate (BER) performace metric of a optical commuicatio system which cosists of a RoFSO ad a RoF lik coected with a regeerator ode. The orthogoal frequecy divisio multiplexig (OFDM) techique is used i both liks for the sigal trasmissio with phase shift keyig (PSK) format ad the mai mitigatio factors which have bee take ito accout is the atmospheric turbulece effect, the oliear resposivity of the laser diode ad the biasig with oliear clippig oise. umerical results for realistic parameter values are derived cocludig i a closed form mathematical expressio for the estimatio of system s BER. Keywords: BER, OFDM, PSK, Fiber Optics, Free Space Optics, oliear Clippig Effect. PACS: 4.79.Sz, 4.81-i, 9.60.hk. I. ITRODUCTIO Free Space Optics (FSO) ad more specifically RoFSO is a very attractive ad alterative solutio i the absece of optical fiber liks, for the itercoectio of a cetral statio to several B-17

2 AUSIVIOS CHORA, VOL. 5, 014 remote cellular base statios. The wide variety of applicatios of this techology is due solely to the high bit rates, the licese free spectrum, the high security level ad the ease of deploymet. O the other had, their efficiecy depeds strogly o the weather coditios such as rai, fog, sow, atmospheric turbulece etc. ad the air compositio like dust, smoke ad other aerosol particulate matter. All these effects icrease the absorptio, scatterig ad refractive idex fluctuatios of the medium, degradig the received sigal quality [1]-[13]. The trasmissio of radio sigals through optical fiber cables, simply kow as radio over fiber or RoF [11], facilitates the wireless access reachig higher capacity levels with sigificat lower sigal atteuatio compared to the atmospheric path. Particularly, the total losses due to the trasportatio of optical sigal through the fiber medium is of the order of 0. db/km reducig the eed of relay odes, while for the atmospheric propagatio losses rage from 0. to more tha 5 db/km depedig o the weather coditios. However, optical fiber trasmissio requires the availability of fiber cable ifrastructure ad thus augmetatio of the total cost, [1]-[]. The aforemetioed effect of the atmospheric turbulece is decreasig sigificatly the FSO lik s performace ad causes the well kow scitillatio effect which results i irradiace fluctuatios at the receiver s side. May statistical distributio models have bee proposed i order to model these sigal s fluctuatios accordig to the turbulece stregth. I this work, we cosider the K ad egative expoetial (E) distributio models which are suitable for cases with strog ad saturate atmospheric turbulece coditios, respectively [14]-[17]. OFDM is a multicarrier modulatio techique which offers importat beefits compared to sigle carrier schemes such as higher spectral efficiecy, robustess agaist frequecy selective fadig ad elimiatio of co-chael ad itersymbol iterferece. Thus, this techique, has gaied popularity i may applicatios, like digital subscriber lies (DSL), wireless local area etworks (WLA), advaced cellular mobile etworks, etc. However, the OFDM sigal exhibits high peak to average power ratios (PAPR) ad is very sesitive to may oliear effects [18]-[4]. Thus, i this work, we preset a dual hop optical commuicatio system which cosists of a RoFSO segmet ad a RoF lik coected with a decodig ad forward (DF) regeerator ode. The sigal propagates i each lik usig, the PSK modulatio format for each subcarrier of the OFDM scheme. The received sigal i the DF ode is recogized, regeerated ad retrasmitted by eglectig the additive oise iserted i the first part of the whole wireless optical system. So, by cosiderig as mai mitigatio factors, the atmospheric turbulece ad the additive distortio of the biasig ad oliear clippig (BAC) process for the RoF segmet, we coclude to a closed form mathematical expressio for the estimatio of the BER of the whole relayed optical wireless ad fiber commuicatio lik [11], [18]-[0]. II. AVERAGE BER FOR THE WIRELESS PART OF THE OPTICAL COMMUICATIO LIK The optical commuicatio system uder cosideratio cosists of two segmets. For the first part, we assume a terrestrial turbulet wireless optical path betwee the trasmitter ad the B-18

3 DF relay ode, while a optical fiber which coects the DF ode with the receiver of the whole lik, stads for the secod part. The iformatio trasmissio is carried out by usig the OFDM techique which is adopted i both liks. I this multiple subcarrier modulatio (MSM) scheme, the iitial high data rate streams are split ito lower rate parallel streams which are cosequetly modulated ito orthogoal arrowbad subcarriers, each oe mapped accordig to a modulatio format. I our case, the PSK format is chose. The OFDM sigal, after the upcoversio to the carrier frequecy f c, just before the laser diode is give as [11], [19], [0]: ( t) s( t) X exp[ i( + πf c) t] for 0 t Ts s OFDM ω < (1) 0 0 where ω π/t s, 0,, -1, is the agular frequecy of each orthogoal subcarrier, T s is the duratio of each OFDM symbol ad X stads for the complex data symbol of the th subcarrier coded with Gray code mappig from a 16 ad 64 PSK costellatio. The trasmitted optical power P(t) from the laser diode LD, ca mathematically be expressed with the followig expressio, [11], [19], [0]: 3 P ( t) Pt 1+ ms( t) + a3 ms( t) () 0 0 where, P t, is the average trasmitted optical power, a 3 stads for the third order oliearity coefficiet of the LD ad m is the optical modulatio idex (OMI) per subcarrier, defied as m I/(I b -I th ), with I beig the variatio of the laser drivig curret aroud a bias poit ad I b, I th, stad for the bias ad threshold laser currets, respectively. The received optical sigal at the receiver of the DF ode, depeds strogly o the turbulece effect after ad is give through the relatio P r (t)p(t)l tot I+(t), where L tot stads for the total losses caused by the atmospheric propagatio, (t) is the additive white Gaussia oise (AWG) of the chael, ad I represets the istataeous ormalized irradiace at the receiver which fluctuates rapidly due to the scitillatio effect caused by the atmospheric turbulece pheomeo. The atmospheric turbulece represets a sigificat mitigatio factor for the performace of the terrestrial wireless optical liks. The radom spatial ad temporal refractive idex variatios of the propagatio path, cause fluctuatios of the irradiace level at the receiver ad cause the so-called scitillatio effect. I order to estimate these itesity fluctuatios, may statistical models have bee proposed based o the turbulece stregth. Here, we examie the cases of strog or saturate turbulece coditios which ca be modeled accurately with the K or E distributio, respectively, [14]-[17]. Thus, the probability desity fuctio (PDF) for the ormalized irradiace I of the K-distributio model is give as [14], [15]: B-19

4 AUSIVIOS CHORA, VOL. 5, 014 a+ 1 ( a) ( ai) a a fi( I) I Ka 1 (3) Γ where Γ(.) is the gamma fuctio, K x (.) is the modified Bessel fuctio of the secod kid ad order x, α depeds o the turbulece stregth, i.e. larger values of α correspod to weaker turbulece ad I is the ormalized irradiace. Additioally, the correspodig PDF for the E distributio is give as, [16], [17]: f I ( I) ( I) exp (4) At the photo detector (PD) of the receiver at the DF relay ode, the geerated curret is give as, [11]: 3 i( t, I) I0 1+ m s( t) + a3 m s( t) + opt( t) (5) 0 0 where I 0 ρl tot P t I is the dc of the received photocurret i(t,i), ρ is the PD s resposivity, while opt is the AWG with zero mea ad variace 0 /, with 0 4K B TF/R L +qi 0 +I 0 (RI). I this equatio, K B is the Boltzma s costat, T is the temperature, F is the electroic receiver amplifier oise figure, R L is the load resistor at the PD s side, q is the electro charge ad RI stads for the relative itesity oise from the laser. Thus, the received istataeous carrier to oise plus distortio for each subcarrier of the OFDM, CDR, is give accurately by the followig approximate formula as, [11], [19], [0]: ( I) m ρ L P I (6) CDR 0 S σ AV IMD tot t ([ T ] + [ ] ) where the symbol [.] AV deotes the average value ad σ IMD stads for the iter-modulatio distortio (IMD), due to the oliear respose of the LD, which affects the specific th subcarrier amog equally spaced subchaels of the OFDM scheme ad depeds o the third order oliearity coefficiet, a 3, ad the OMI m, for each OFDM subcarrier [11], [19], [0]. From (4), the expected value [CDR ] EX, ca be estimated, cosiderig the expected value of the ormalized irradiace, I, i.e. E[I], as, [11], [19], [0]: AV [ ] ( mρl PE[ I] ) CDR EX 0 s σ AV IMD AV tot t ([ T] + [ ] ) (7) The BER of a commuicatio system is a sigificat metric for the estimatio of its performace. For a optical OFDM commuicatio system which is usig M-PSK modulatio format the BER is give as, [19], [0], [5]: B-0

5 ( ) ( ) 1 1 π Pb, FSO erfc CDR I si log M 0 M (8) where erfc(.) is the complemetary error fuctio ad M is the PSK modulatio format parameter. Takig ito accout (8), ad the PDF of the suitable distributio model, i.e. the K or the E, the average BER for all the subcarriers of the M-PSK OFDM RoFSO is give as [19]: [ P ] 1 π, FSO erfc CDR AV ( M) si log M b 0 0 ( I) f ( I)dI I (9) ext, by substitutig i (9) the PDF of the K-distributio model, i.e. Eq. (3), we coclude to the followig expressio: a+ 1 a b, FSO ( ) ( ) erfc CDR, AV K a Γ a log M 0 0 M [ P ] a π ( ) I si I K ( ai) di (10) while, from (9), usig the PDF of the E distributio, i.e. Eq. (4), we coclude to the followig expressio: [ P ] 1 π, FSO ( ) erfc CDR exp AV, E log M M b 0 0 ( I) si ( I) di (11) By trasformig the erfc(.), K x (.) ad exp(.) fuctios with the correspodig Meijer fuctios oes, [6], the itegral of (10) ca be solved ad we coclude to the followig closed form mathematical expressio for the estimatio of the average BER of a M-PSK OFDM RoFSO lik uder strog turbulece coditios: [ P ] b, FSO AV, K Γ 3 a 1 1 a a π,4 π,, 0, 0.5, 1 G [ ] 5, 16a si CDR EX (1) 0 M ( a) log ( M) 0, 0.5 m, where G p,q[] stads for the Meijer-fuctio that is a stadard built i fuctio which ca be evaluated with most of the well kow mathematical software packages. Furthermore, this fuctio ca be trasformed to the familiar hypergeometric fuctios, [6]. Additioally, from (1), we estimate the followig closed form mathematical expressio for the estimatio of the average BER of a M-PSK OFDM RoFSO lik uder turbulece coditios modeled with the E distributio: [ P ] π [ ] ( ) 1, 0, 0.5, b 3,, FSO G 4si CDR AV, E EX log M 0 0, 0. 5 M π 1 (13) B-1

6 AUSIVIOS CHORA, VOL. 5, 014 III. BER FOR THE OPTICAL FIBER PART OF THE COMMUICATIO LIK I the secod part of the optical commuicatio system, betwee the DF ode ad the receiver, the sigal propagates through a optical fiber. The OFDM scheme is used agai with the same modulatio format of M-PSK for each subcarrier. The OFDM sigal, after the iverse fast Fourier trasform (IFFT), is bipolar i geeral ad caot be applied directly to a itesity modulatio/direct detectio (IM/DD) system. Thus, a dc offset has to be added, i order to produce a suitable uipolar curret to drive the laser diode ad prevet the clippig of egative peaks. So, the istataeous evelope of the OFDM sigal is Gaussia distributed with mea µ ad variace, σ. However, the high PAPR of the OFDM sigal is a domiat disadvatage costraied by the fiite liear respose rage for iput amplitudes of the laser diode. Durig the biasig ad clippig of the dc compoet after the FFT, a oliear clippig distortio isertio is ievitable. For such a optical OFDM commuicatio system usig M-PSK modulatio format for optical fiber trasmissio icludig the BAC process, the total BER is expressio (8) modified for this case as follows, [5]: 1 1 π Pb, OF ( ) erfc γ e, si log (14) M 0 M where γ e stads for the effective SR give as γ γ γ [( + γ )( 1+ γ ) + γ ] e c d 1, with γ d the SR at the receiver, γ c the ratio of the trasmittig sigal, from the regeerator ode, over the oliear clippig oise, ad γv DC /σ Ν is the ormalized clippig level with V DC beig the biasig voltage. Moreover, the value of γ c is give as [18]: c d γ c γ γe Q π γ e π γe γ ( γ) + ( γ + 1) Q( γ) ( γ + 1) Q( γ) π [ ] [ 1 Q( γ) ] (15) IV. THE TOTAL AVERAGE BER OF THE WHOLE RELAYED OPTICAL LIK The total average BER of the whole relayed optical system ca be estimated through the obtaied expressios i Eqs. (1)-(15). The total BER of the whole optical commuicatio lik is estimated as, [7], [8]: P ] (16) b, Total Pb, OF + [ Pb, FSO] AV Pb, OF[ Pb, FSO AV Thus, for the case of strog turbulece coditios, i.e. K-distributio model, the BER of the whole relayed optical system with M-PSK OFDM RoFSO ad optical fiber lik with BAC process, is give by substitutig (1) ad (14) i (16), ad we coclude to the followig closed form mathematical expressio: B-

7 3 a ( ) ( ) ( ) ( ) Ω+ Ψ 1 π 1 Pb, Total, turb turb 1 Ω (17) log M 0 Γ a log M 0 log M 0 where the subscript turb, stads either for the E or K-distributio model, i.e. E or K subscript, respectively, for the atmospheric turbulece effect, [ ] 1,4 16 CDR a a EX π,,0,0.5,1 Ψ π K G5, si, Ω erfc γ a M e, si 0, 0.5 M, [ ] π 0, 0.5, 1 ΨE G3, 4si CDR EX M 0, 0.5. ad V. UMERICAL RESULTS I this sectio usig expressios (1)-(14) ad (17), we preset the umerical results for the total average BER of the dual hop optical OFDM commuicatio system uder the K ad E turbulece, for commo parameter values. The parameter value γ of the BAC process was take equal to 6, 9 ad 1 db for optimizatio accordig to Ref. [5], while the modulatio for the M-PSK format is equal to 16 ad 64. The variable quatities for the estimatio of the BER performace is the CDR ad SR at the receivers of the FSO ad the optical fiber lik, respectively. It is obvious that these quatities ca vary idepedetly, but for simplificatio, here, we assume that they take the same values for both liks. FIGURE 1. BER estimatio for the 16-PSK OFDM system with K distributio. B-3

8 AUSIVIOS CHORA, VOL. 5, 014 FIGURE. BER estimatio for the 64-PSK OFDM system with K distributio. FIGURE 3. BER estimatio for the 16-PSK OFDM system with E distributio. B-4

9 FIGURE 4. BER estimatio for the 64-PSK OFDM system with E distributio. I Figures 1 ad we preset the results of BER for strog turbulece coditios usig the K distributio ad we observe that for low SR ad CDR values the atmospheric turbulece is the major impairmet factor for the BER performace. For higher SR ad CDR values the BAC process startig to play a sigificat role for the BER performace. The higher values of the BAC process parameter, coserve the BER at higher levels despite the large SR ad CDR. I Figures 3 ad 4 we preset the correspodig results for the case of saturated turbulece coditios with E beig a suitable model for such coditios. Similarly to the previous figures, we ca clearly see that as parameter γ icreases, the BER icreases too. I all the above figures, it is also clear that for higher values of modulatio format parameter M, the performace of the system becomes worse. VI. COCLUSIOS I this work we studied a hybrid OFDM optical system which cosists of a relayed RoFSO ad RoF lik which are usig a M-PSK OFDM scheme. For the wireless lik, we assume that the domiat performace mitigatio factor is the atmospheric turbulece effect, which is modeled either with the K or E distributio, while for the optical fiber lik, the BAC process effect. For these cases we derive closed form mathematical expressios for the estimatio of the average BER of each part of the optical commuicatio lik ad for the whole system, as well. Fially usig these expressios we preset the correspodig umerical results for realistic parameter values. B-5

10 AUSIVIOS CHORA, VOL. 5, 014 VII. REFERECES 1. Z. Ghassemlooy, W.O. Popoola, "Terrestrial Free-Space Optical Commuicatios", book chapter i Mobile ad Wireless Commuicatios: etwork Layer ad Circuit Level Desig, S. Ait Fares ad F. Adachi (Ed.), ISB: , ITech, H. Heiger, O. Wilfert, A Itroductio to Free-Space Optical Commuicatios, Radioegieerig, 19,, 010, W.O. Popoola, Z. Ghassemlooy, E. Leitgeb, BER ad Outage Probability of DPSK Subcarrier Itesity Modulated Free Space Optics i Fully Developed Speckle, J. of Comm., 4, 8, , D. Tsoev, S. Siaovic ad H. Haas, Complete Modelig of oliear Distortio i OFDM-Based Optical Wireless Commuicatio, J. Lightwave Techology, Vol. 31, o. 18, 013, pp T. Kamalakis, T. Sphicopoulos, S. S. Muhammad, ad E. Leitgeb, Estimatio of the power scitillatio probability desity fuctio i free-space optical liks by use of multicaoical Mote Carlo samplig, Opt. Lett., Vol. 31, o. 1, 006, pp W. Gappmair, S. Hrailovic, E. Leitgeb, Performace of PPM o terrestrial FSO liks with turbulece ad poitig errors, IEEE Commu. Lett., Vol. 14, o. 5, 010, pp H.G. Sadalidis, Coded Free-Space Optical Liks Over Strog Turbulece ad Misaligmet Fadig Chaels, IEEE Trasactios o Wireless Commuicatios, Vol. 59, o. 3, 011, pp A. Katsis, H.E. istazakis, ad G.S. Tombras, Bayesia ad frequetist estimatio of the performace of free space optical chaels uder weak turbulece coditios, J. Frakli Ist., Vol. 346, 009, pp W. Gappmair ad S.S. Muhammad, Error performace of PPM/Poisso chaels i turbulet atmosphere with gamma-gamma distributio, IET Electroics Letters, Vol. 43, o. 16, art. o , L.C. Adrews, R.L. Phillips, C.Y. Hope, Laser beam scitillatio with applicatios. SPIE Optical Eg. Press, Belligham, WA A. Bekkali, C.B. aila, K. Kazaura, K. Wakamori, M. Matsumoto, Trasmissio Aalysis of OFDM- Based Wireless Services Over Turbulet Radio-o-FSO Liks Modeled by Gamma-Gamma Distributio, IEEE Photoics Joural,, 3, 010, pp H.E. istazakis ad G.S. Tombras, O the use of wavelegth ad time diversity i optical wireless commuicatio systems over gamma gamma turbulece chaels, Optics & Laser Techology, Vol. 44, 01, pp B. Epple, Simplified Chael Model for Simulatio of Free-Space Optical Commuicatios, IEEE/OSA J. Opt. Commu. etw., Vol., o. 5, 010, pp H.E. istazakis, A.D. Tsigopoulos, M.P. Haias, C.D. Psychogios, D. Marios, C. Aidiis, G.S. Tombras, Estimatio of Outage Capacity for Free Space Optical Liks Over I-K ad K Turbulet Chaels, Radioegieerig, Vol. 0, o., 011, pp H.G. Sadalidis, T.A. Tsiftsis, Outage probability ad ergodic capacity of free-space optical liks over strog turbulece, El. Lett., 44, 1, H.E. istazakis, A Time-Diversity Scheme for Wireless Optical Liks Over Expoetially Modeled Turbulece Chaels, Elsevier, Optik -Iteratioal Joural for Light ad Electro Optics, Vol. 14, Iss. 13, 013, pp H.E. istazakis, V.D. Assimakopoulos, ad G.S. Tombras, Performace Estimatio of Free Space Optical Liks Over egative Expoetial Atmospheric Turbulece Chaels, OPTIK-Iteratioal Joural for Light ad Electro Optics, Vol. 1, 011 pp L. Che, B. Krogold ad J. Evas, Theoretical Characterizatio of oliear Clippig Effects i IM/DD Optical OFDM Systems, IEEE Trasactios o Commuicatios, Vol. 60, 01, o H.E. istazakis, A.. Stassiakis, S.S. Muhammad ad G.S. Tombras, BER Estimatio for Multi Hop RoFSO QAM or PSK OFDM Commuicatio Systems Over Gamma Gamma or Expoetially Modeled Turbulece Chaels, Elsevier Optics & Laser Techology, Vol. 64, 014, pp B-6

11 0. H.E. istazakis, A.. Stassiakis, H.G. Sadalidis ad G.S. Tombras, QAM ad PSK OFDM RoFSO over M-Turbulece Iduced Fadig Chaels, IEEE Photoics Joural, Vol. 7, o. 1, DOI: /JPHOT , Q. Shi, Asymptotic Clippig oise Distributio ad its Impact o M-ary QAM Trasmissio Over Optical Fiber, IEEE Tras. Commu., 43, 1995, pp A. Mostafa ad S. Hrailovic, I-Field Demostratio of OFDM-Over-FSO, IEEE Photoics Techology Letters, 4, 8, 01, pp S. Dimitrov, S. Siaovic ad H. Hass, Clippig oise i OFDM-Based Optical Wireless Commuicatio Systems, IEEE Tras. Commu., Vol. 60, o. 4, 01, pp A.J. Lowery, L.B. Du ad J. Armstrog, Performace of Optical OFDM i Ultralog-haul WDM Lightwave Systems, IEEE J. Lightwave Techology, Vol. 5, o. 1, pp , J. Proakis, Digital Commuicatios, 4 th Editio, McGraw-Hill, V.S. Adamchik ad O.I. Marichev, The Algorithm for Calculatig Itegrals of Hypergeometric Type Fuctio ad its Realizatio i Reduce System, Proc. Itl Coferece o Symbolic ad Algebraic Computatio, Japa, 1990, pp E. Morgado, I. Mora-Jiméez, J. J. Viagre, J. Ramos ad A.J. Caamaño, Ed-to-Ed Average BER i Multihop Wireless etworks over Fadig Chaels, IEEE Trasactios o Wireless Commuicatios, Vo. 9, 010, o H.E. istazakis, A.. Stassiakis, G.S. Tombras, S.S. Muhammad ad A.D. Tsigopoulos, K Modeled Turbulece ad oliear Clippig for QAM OFDM with FSO ad Fiber Serially Liked, 0th Iteratioal Coferece o Microwaves, Radar, ad Wireless Commuicatios MIKO-014, IEEE Coferece Proceedigs, ieeexplore.ieee.org, ISB: , DOI: /MIKO , 014, pp B-7

New Performance Results for QAM OFDM RoFSO Over K and Exponentially Modeled Turbulence Channels

New Performance Results for QAM OFDM RoFSO Over K and Exponentially Modeled Turbulence Channels New erformace Results for QAM OFDM RoFSO Over K ad Expoetially Modeled Turbulece Chaels H.E. Nistazakis a, M.. Nios a, A.N. Stassiakis a, A.D. Tsigopoulos b, ad G.S. Tombras a a Departmet of Electroics,